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X-ray Based in Situ Investigation of Silicon Growth
Mechanism Dynamics - Application to Grain and Defect
Formation
Hadjer Ouaddah, M. Becker, Thècle Riberi-Béridot, M.G. Tsoutsouva, V.
Stamelou, Gabrielle Regula, Guillaume Reinhart, Isabelle Perichaud, F.
Guittonneau, Laurent Barrallier, et al.
To cite this version:
Hadjer Ouaddah, M. Becker, Thècle Riberi-Béridot, M.G. Tsoutsouva, V. Stamelou, et al.. X-ray
Based in Situ Investigation of Silicon Growth Mechanism Dynamics - Application to Grain and Defect
Formation. Crystals, MDPI, 2020, 10 (7), pp.555. �10.3390/cryst10070555�. �hal-02910279�
Review
X-ray Based in Situ Investigation of Silicon Growth
Mechanism Dynamics—Application to Grain and
Defect Formation
Hadjer Ouaddah1, Maike Becker1 , Thècle Riberi-Béridot1, Maria Tsoutsouva1,
Vasiliki Stamelou1, Gabrielle Regula1, Guillaume Reinhart1, Isabelle Périchaud1, Fabrice Guittonneau2 , Laurent Barrallier2, Jean-Paul Valade3, Alexander Rack3 , Elodie Boller3, José Baruchel3and Nathalie Mangelinck-Noël1,*
1 Aix Marseille Univ, Université de Toulon, CNRS, IM2NP, 13397 Marseille, France;
[email protected] (H.O.); [email protected] (M.B.); [email protected] (T.R.-B.); [email protected] (M.T.); [email protected] (V.S.); [email protected] (G.R.); [email protected] (G.R.); [email protected] (I.P.)
2 Arts et Metiers Institute of Technology, MSMP, HESAM Université, F-13617 Aix-en-Provence, France;
[email protected] (F.G.); [email protected] (L.B.)
3 ESRF—The European Synchrotron, CS40220, 38043 Grenoble CEDEX 9, France; [email protected] (J.-P.V.);
[email protected] (A.R.); [email protected] (E.B.); [email protected] (J.B.) * Correspondence: [email protected]; Tel.:+33-491-28-87-37
Received: 3 June 2020; Accepted: 27 June 2020; Published: 30 June 2020
Abstract:To control the final grain structure and the density of structural crystalline defects in silicon (Si) ingots is still a main issue for Si used in photovoltaic solar cells. It concerns both innovative and conventional fabrication processes. Due to the dynamic essence of the phenomena and to the coupling of mechanisms at different scales, the post-mortem study of the solidified ingots gives limited results. In the past years, we developed an original system named GaTSBI for Growth at high Temperature observed by Synchrotron Beam Imaging, to investigate in situ the mechanisms involved during solidification. X-ray radiography and X-ray Bragg diffraction imaging (topography) are combined and implemented together with the running of a high temperature (up to 2073 K) solidification furnace. The experiments are conducted at the European Synchrotron Radiation Facility (ESRF). Both imaging techniques provide in situ and real time information during growth on the morphology and kinetics of the solid/liquid (S/L) interface, as well as on the deformation of the crystal structure and on the dynamics of structural defects including dislocations. Essential features of twinning, grain nucleation, competition, strain building, and dislocations during Si solidification are characterized and allow a deeper understanding of the fundamental mechanisms of its growth. Keywords: silicon; growth; grains; defects; twins; strain; dislocations; X-ray radiography; X-ray topography; Bragg diffraction imaging
1. Introduction
Current research on crystalline Si used for photovoltaic solar panels focuses on several key targets from silicon purification to cell manufacturing including the silicon ingot fabrication process step. Several alternative methods are proposed to optimize the Si growth process to increase the production yield while reducing the costs. However, this cannot be done at the expense of the crystalline quality of the final ingot as the performance of the solar cells is directly related to it. Three main methods aim at mastering the initial grain nucleation and defect generation from the first stage of solidification: the dendritic casting method [1,2], the cast mono solidification (cm-Si) [3–5], and the high performance Crystals 2020, 10, 555; doi:10.3390/cryst10070555 www.mdpi.com/journal/crystals
multi-crystalline silicon (HP mc-Si) [6]. HP mc-Si and cm-Si techniques are both used in the industry and allow producing ingots with a lower dislocation density compared to the conventional mc-Si while allowing the use of low-cost casting solidification methods. In the case of cm-Si, a pavement of monocrystalline seeds is placed on the bottom of the crucible in order to take up the initial orientation of the seed [3]. However, cm-Si efficiencies are still limited due to the presence of structural defects such
as parasitic grain nucleation on the walls of the crucible [4,7], twin formation and more importantly, dislocations. The latter can be either arranged in cellular patterns, in the entire cm-Si ingot and are known as background dislocations [8] or generated on the top of the seeds [9,10], at their junctions on precipitates [10] and propagate vertically along the growth direction [9,11–16] generating the formation of sub-grain boundaries. HP mc-Si technique is based on a very different approach aiming at obtaining small-size and uniform grains at the initial stage of solidification with random angle and coherent grain boundaries [6,17]. This results in low density of dislocation clusters thanks to blocking mechanisms by which dislocations that nucleate at the beginning of the crystallization process cannot propagate further along the growth of the ingot. Recent work by Stokkan et al. [17] highlighted the necessity to control the first nucleation events to improve the crystalline quality. It is worth noting that in the other main process in the market, Czokralski (Cz), which aims at the of the fabrication of monocrystalline ingots the issue of dislocations and structural defects remains a main concern especially when one wants to improve the method (higher volumes, faster process, reusable crucibles and seeds, etc.) [18,19].
Grain boundaries and dislocations can severely limit the conversion efficiency of solar cells by reducing the minority carrier lifetime [20–23]. Dislocations remain one of the most important efficiency
limiting defects in Si solar cells, because they can act as preferential segregation sites for impurities, ultimately reducing the carrier lifetime [11,16,24–26]. At a higher scale, sub-grain boundaries and grain boundaries of high planar mismatch can be more detrimental than high symmetry grain boundaries such as symmetric coincidence site lattice (CSL) twin boundaries, also due to decoration by impurities [27]. Various studies show that the crystalline quality of an ingot in general and the twin relationship between the grains in particular can have a significant impact on the photoelectric properties [27–29]. Moreover, although it has been shown that perfect symmetricP3 twins have no major impact on the photovoltaic properties, the repetition of twinning has important consequences for the final grain structure and distribution of crystallographic orientations [30,31]. The importance of twinning in the development of the grain structure has been highlighted for very different solidification processes including directional mc-Si solidification [32] and ribbon growth [33]. Another issue is to control and lower the density of strained regions of the crystal structure that can be at the origin of dislocation emission during growth or subsequent cooling down and solar cell fabrication processes. Recent molecular dynamics simulations of silicon growth highlighted the interrelation between strain field, dislocation generation relatively to the growth direction, and twin nucleation [34]. The control of the formation of structural defects is thus motivated by their direct impact on the PV properties. Such a control is only possible if a thorough understanding of the crystal growth mechanism is achieved. The understanding of the development of the structural defects during growth is limited by the difficulty of accessing, from the ex situ study of the solidified ingots, to the history of defect formation and interrelation. Moreover, these structural defects cover by essence a large scale range (from dislocations to grains).
To answer these issues and key points, benchmark experiments have been proposed to investigate the growth from silicon melt in situ. Characterization of the solidification of an undercooled levitated silicon droplet was performed using an X-ray diffractometer and by recording the droplet surface image using a high-speed video camera [35]. The in situ solidification behavior of Si droplets on silicon wafers was also characterized using IR thermal imaging [36]. Fujiwara et al. [2,37–41] use a confocal scanning laser microscope to carry out in situ observations of crystal growth from silicon melt by providing live images of solid–liquid interface features and of the growth of grains. With this method, a detailed investigation of the Si microstructure during growth has been carried out. X-ray Bragg diffraction imaging (topography) is also used to characterize crystalline defects [26]. More information
and explanation on this technique will be given in the following as this is a method of choice to characterize crystalline defects that we use in our experiments. It is worth mentioning the pioneer work of Pr. Chikawa [42,43] who conducted in situ X-ray topography during melting and solidification of silicon.
Starting from the considerations that in situ characterization of silicon growth constitutes an invaluable tool to understand the crystal growth phenomena and the formation of structural defects, we implemented in situ X-ray imaging during the solidification of silicon. The GaTSBI (Growth at high Temperature observed by Synchrotron Beam Imaging) tool was developed to fulfil this objective. This present paper is a review paper of our major results concerning the formation of grains, twinning, and competition [44–53] using advanced in situ and complementary ex situ characterization methods. In situ X-ray imaging and methods are described in detail. Our results concerning dislocations and the effect of impurities are not presented in detail here. Results concerning the effect of Cu, C, and O impurities can be found in [53].
2. Materials and Methods 2.1. GaTSBI Tool
GaTSBI is a unique device with which the solidification processes can be characterized in real time during growth. It is a specially designed instrument composed of a high temperature (up to 2073 K) directional solidification (DS) furnace employed in conjunction with synchrotron radiation X-ray imaging techniques (Bragg diffraction imaging—topography and radiography).
2.1.1. Directional Solidification Furnace
The DS furnace is based on two heating graphite resistors that are inside a vacuum chamber under dynamic vacuum (≈10−6 mbar). The powers of the heating resistors are regulated by the external controller of the DS furnace. The control loop uses the temperature values measured by pyrometers pointing on the heaters.
The typical sequence used in our experiments concerning silicon solidification is the following: • Step 1—Preheating: the silicon sample cut inside ingots of different origins is heated by applying
the same temperature to the bottom and top resistances of the furnace (isotherm conditions) up to 1373 K.
• Step 2—Temperature gradient: a vertical temperature gradient is applied by imposing a controlled temperature difference between both heaters. The same temperature gradient is maintained until step 5.
• Step 3—Partial melting: the sample is partially melted (Si melting temperature: 1687 K). This is monitored by imaging during the heating phase. A seed crystal, preserving the initial orientation of the sample, is kept within the field of view of the X-ray imaging.
• Step 4—Solidification: both heaters are cooled at the same controlled cooling rate until the region of the silicon sample observed within the field of view is fully solidified. The same cooling rate is applied on both heaters to maintain a constant temperature gradient during solidification. In some particular cases, not reported in this manuscript, solidification is conducted by pulling the sample downwards. In both cases, the solidification is directional in the upward direction due to the imposed vertical temperature gradient.
• In some experiments, a new cycle is started again from step 3.
• Step 5—Controlled cooling down: the sample is cooled down until 923 K by applying cooling rates of −13 and −10.4 K/min to the top and bottom heaters, respectively.
• Step 6—Cooling down to room temperature: free cooling down takes place from 923 K as temperatures below this value cannot be controlled by design of the furnace.
2.1.2. Crucible Assembly
Two thin pyrolytic boron nitride (BN) plates serve as crucible material. One of the BN plates has a mechanically machined slot with the dimensions of the samples. The typical sample dimensions are as follows: length 40 mm, width 6–8 mm, and thickness about 0.3 mm. The front and back sides of the sample are in contact with the crucible walls. The crucible assembly can be seen for example in Figure1b of Reference [45]. The two BN plates are held together by two Molybdenum clips so that it applies a pressure on the main surfaces of the samples. In a further step, the silicon sample housed in the BN crucible, is introduced inside the DS furnace.
2.1.3. Origin of the Silicon Samples
The initial monocrystalline Si samples are cut from double side mechano-chemically polished intrinsic (resistivity beyond 5000Ω.cm) float-zone (FZ) wafers with a diameter of 50.8 mm, or from conventional Cz industrial ingots (typical oxygen concentration: 0.5–1 × 1018 at/cm3). The FZ samples provided by SIL’TRONIX Silicon Technologies are produced with 9N purity by the float-zone technique and contain no visible dislocations at the beginning of the experiments. Oxygen and carbon concentrations are below<1015at cm−3and metallic impurity contamination is limited to 1011at/cm−3. 2.1.4. X-Ray Imaging
The GaTSBI set-up is not only a DS device but is specifically designed to allow X-rays to cross the furnace windows and elements up to the sample without deleterious absorption and diffraction of the incoming X-rays. The beam crosses the entry and exit vacuum chamber windows that are made out of 0.5 mm thick aluminum. Additional vitreous carbon plates are positioned in the beam path serving as insulation of the furnace. As a consequence, a high photon flux is needed to ensure good quality imaging. This is one of the reasons, although not exclusive why the experiments are conducted using synchrotron X-ray generated at the European Synchrotron Radiation Facility.
A schematic drawing of the general imaging assembly can be found for example in Figure1a in Reference [45]. During the experiments, the sample inside the DS furnace is constantly illuminated by the X-ray synchrotron polychromatic beam, which avoids variations of the heat load due to the beam. Indeed, the polychromatic beam creates heat load which is minimized with filters introduced in the beam before reaching the DS furnace. A compromise between minimized heat load and sufficient photon flux needs to be achieved resulting in the utilization of Al filters between 0.5 and 0.7 mm in our experiments. On the one hand, a sufficient photon flux level is assessed qualitatively by checking that the solid–liquid interface can be characterized with a counting time not higher than 1 s which is required to be able to follow its dynamic evolution during solidification. On the other hand, variations of the heat load need to be minimized for two reasons: it is sufficient to modify the thermal field inside the sample, it modifies the behavior of the crystals used in the post-monochromator that will be described in the following.
Two imaging techniques, X-ray radiography and X-ray Bragg diffraction imaging (topography), are used during the steps described in Section2.1(heating, solidification, and cooling down of the samples). Both imaging techniques are non-destructive.
2.1.5. X-Ray Radiography
In the X-ray radiography mode, the direct beam passing through the sample is used to record images of the growing solid–liquid interface. A polychromatic beam is needed for the diffraction imaging mode, whereas a monochromatic beam is needed in the case of X-ray radiography to increase the legibility of the images. First, the polychromatic direct X-ray beam goes through the sample and exits the furnace vacuum chamber. The polychromatic direct beam is then turned monochromatic at a target energy, empirically determined as explained in the following, using a vertically diffracting Si
(111) double-crystal monochromator. Finally, images are recorded using a camera equipped with a scintillator to interface X-rays with the camera matrix detector.
X-ray attenuation contrast is the dominating imaging modality used in the frame of this work. Considering the use of synchrotron light sources, an additional modality present is related to the refraction at interfaces, frequently termed propagation-based X-ray phase contrast [54,55]. Due to the rather coarse pixel sizes used and to the relatively short distance between sample and detector, the effect of phase contrast is not pronounced in the images shown in this work and therefore only mentioned for the sake of completeness. Thus, the contrast in X-ray imaging radiographs shown here is mainly due to the differential absorption of the different sample regions. The Beer–Lambert law determines the absorption of a material (Equation (1)). Incident monochromatic beam intensity is exponentially attenuated as a function of the thickness, of the nature of the sample and of other materials crossed by the incident beam:
It=I0e −µ
i(T,C).l (1)
where Itis the transmitted intensity, I0is the incident intensity, µiis the linear absorption coefficient (in m−1), which depends on the temperature T and on the composition C while l is the thickness. The linear absorption coefficient is a function of the density of the material.
As the absorption of other materials crossed by the beam is constant, the only contribution to the image contrast comes from the sample. In the case of a pure material such as silicon, a difference in transmission, and therefore a contrast in the images, is expected only from the density difference between the solid (2.33 g/cm3) and the liquid (2.56 g/cm3) close to the melting temperature T
m. This density difference is only 9%. The use of monochromatic light is essential to exploit the weak attenuation contrast originating from this density difference between the solid and the liquid silicon phases in the radiography images. The choice of the monochromatic energy used for X-ray radiography is based on a compromise between an acceptable transmission and a contrast allowing to reveal the solid–liquid interface features. During our experiments, it was empirically determined that an energy of 17.5 keV must be used, which corresponds to a transmission of 63% of the liquid phase. However, the contrast between the solid and liquid phase is then only about 4%. Due to the limited density difference and the compromise in energy, the solid–liquid interface is hardly distinguishable on the raw images oppositely to the case of alloys for which a higher density difference is obtained because of the presence of several phases and of solute [56]. In addition, the legibility of the images is considerably affected
by the unavoidable non-uniform profile of the X-ray beam and by the surface inhomogeneity of the silicon crystals in the post-monochromator. As a consequence, image processing is absolutely needed.
The image processing is based on the principle of pixel by pixel division and is performed using the ImageJ software [57]. By dividing two images recorded at different times, the areas that remain
in the same state (liquid or solid) have the same transmission and corresponding pixel values in the images, thus the result of the division is equal to 1. As the liquid transmission is lower than the solid transmission, zones that change from liquid to solid appear in lighter grey (the result of the division is lower than 1), and zones that change from solid to liquid appear in darker grey (the result of the division is higher than 1).
Two types of treatment are used:
• Division by the first image taken after cooling starts:
For this treatment, all images of the solidification sequence are divided by a single reference image recorded just after applying the cooling rate. A typical image resulting from this treatment is shown in Figure1a, α, β, and δ indicate the region of the regrown interface, the fully solid and liquid regions, respectively. A light grey area is observed above the fully solid zone (γ in Figure1a). This area corresponds to a zone constituted of solid and liquid that exists within the thickness of the sample at the level of the solid–liquid interface. This is first due to the fact that the images correspond to a projection of the sample volume hit by the beam and second to the orientation of the solid–liquid
interface which is not necessarily parallel to the incident beam. An illustration of a possible solid–liquid interface side view configuration is depicted in the sketch in Figure1b. At the level of the solid–liquid interface region, the beam goes through both solid and liquid regions which explains the grey level neither corresponding to a fully solid volume nor to a fully liquid volume.
This treatment allows following the evolution of the solid–liquid interface during growth. Dynamic features can be observed, and the growth velocity of the solidification front can be measured. • Division of two successive images:
For this treatment, each image is divided by the previous one or by an image separated from the current one by a few images only (Figure1c). In this case, the resulting image is less prone to noise and artefact variations in beam intensity with time as for the first treatment. Then, sharper contours are obtained, revealing more details of the solid–liquid interface as can be seen in the close-up in Figure1c which shows more clearly the same grain boundary groove (close-up in Figure1a). The morphology of the interface and of the grain boundary grooves can thus be studied in detail.
Crystals 2020, 10, 555 6 of 25 and artefact variations in beam intensity with time as for the first treatment. Then, sharper contours are obtained, revealing more details of the solid–liquid interface as can be seen in the close-up in Figure 1c which shows more clearly the same grain boundary groove (close-up in Figure 1a). The morphology of the interface and of the grain boundary grooves can thus be studied in detail.
Figure 1. X-ray radiography image recorded during solidification (applied temperature gradient: 30 K/cm and cooling rate of -1 K/min applied on both heaters) from a FZ-Si seed. (a) Image resulting from the pixel by pixel division of the current image by the first image after starting the cooling down (α: seed–regrown interface, β: fully solid region, γ : solid–liquid interface region, δ: fully liquid region). (b) Sketch of the side view. (c) Image resulting from the pixel by pixel division of two successive raw images with a time interval of 3 s and close-up at the level of the interface at the same instant and position as in (a).
The radiography technique allows observing the growth of the interface, measuring the growth velocities, studying the evolution of grain boundary grooves, and the appearance of facets and twins. It provides a non-deformed image of the solid–liquid interface and of the sample. The volume projection effect needs to be taken into account for quantitative measurements (e.g., for the measurements of the facet normal growth rate discussed in Section 3.1 and described in more detail in [48]).
In the experiments presented in the following, the X-ray radiography images are recorded on detectors based on the association of a scintillator to convert X-rays in visible light and of a CCD or CMOS camera detector [58]. An optics giving a good compromise between a large field of view encompassing the whole sample width, a solidification height of about 10 mm, and a sufficient spatial resolution is used. More precisely, two detectors were used. First, a CCD camera developed at the ESRF named FReLoN (Fast Readout Low-Noise) with 2048 × 2048 pixels was used and coupled with an optics giving a 5.8 µm pixel size and a 11.9 × 11.9 mm2 field of view. In our most recent experiments, a detector (sCMOS lens-coupled to a LuAG scintillator) 2048 × 2048 pixels with a nominal pixel size of 6.5 µm2 and a 16 bit dynamic range was used.
Radiography images are generally recorded every 3 s with an exposure time of 1 s which is a sufficient time-resolution to be able to characterize solidification.
2.1.6. X-ray Bragg Diffraction Imaging—Topography
X-ray Bragg diffraction imaging (X-ray topography) is the complementary and essential non-destructive technique used to characterize the grown crystal quality during the same experiment. When the polychromatic beam illuminates the silicon sample installed inside the solidification furnace, diffraction occurs according to Bragg’s law, generating a Laue diffraction pattern in addition to the direct beam exploited for X-ray radiography. The Laue diffraction pattern is constituted of several diffraction spots related to specific lattice planes.
The transmission mode is used i.e., the incident beam is transmitted through the sample and the diffracted beams expose a detector that is placed after the sample. Transmission mode is the only possible one in our experiments as the sample is installed inside the vacuum chamber containing the furnace. The use of a polychromatic beam allows collecting multiple spots from multiple grains in a
Figure 1. X-ray radiography image recorded during solidification (applied temperature gradient: 30 K/cm and cooling rate of −1 K/min applied on both heaters) from a FZ-Si seed. (a) Image resulting from the pixel by pixel division of the current image by the first image after starting the cooling down (α: seed–regrown interface, β: fully solid region, γ: solid–liquid interface region, δ: fully liquid region). (b) Sketch of the side view. (c) Image resulting from the pixel by pixel division of two successive raw images with a time interval of 3 s and close-up at the level of the interface at the same instant and position as in (a).
The radiography technique allows observing the growth of the interface, measuring the growth velocities, studying the evolution of grain boundary grooves, and the appearance of facets and twins. It provides a non-deformed image of the solid–liquid interface and of the sample. The volume projection effect needs to be taken into account for quantitative measurements (e.g., for the measurements of the facet normal growth rate discussed in Section3.1and described in more detail in [48]).
In the experiments presented in the following, the X-ray radiography images are recorded on detectors based on the association of a scintillator to convert X-rays in visible light and of a CCD or CMOS camera detector [58]. An optics giving a good compromise between a large field of view encompassing the whole sample width, a solidification height of about 10 mm, and a sufficient spatial resolution is used. More precisely, two detectors were used. First, a CCD camera developed at the ESRF named FReLoN (Fast Readout Low-Noise) with 2048 × 2048 pixels was used and coupled with an optics giving a 5.8 µm pixel size and a 11.9 × 11.9 mm2field of view. In our most recent experiments, a detector (sCMOS lens-coupled to a LuAG scintillator) 2048 × 2048 pixels with a nominal pixel size of 6.5 µm2and a 16 bit dynamic range was used.
Radiography images are generally recorded every 3 s with an exposure time of 1 s which is a sufficient time-resolution to be able to characterize solidification.
2.1.6. X-Ray Bragg Diffraction Imaging—Topography
X-ray Bragg diffraction imaging (X-ray topography) is the complementary and essential non-destructive technique used to characterize the grown crystal quality during the same experiment. When the polychromatic beam illuminates the silicon sample installed inside the solidification furnace, diffraction occurs according to Bragg’s law, generating a Laue diffraction pattern in addition to the direct beam exploited for X-ray radiography. The Laue diffraction pattern is constituted of several diffraction spots related to specific lattice planes.
The transmission mode is used i.e., the incident beam is transmitted through the sample and the diffracted beams expose a detector that is placed after the sample. Transmission mode is the only possible one in our experiments as the sample is installed inside the vacuum chamber containing the furnace. The use of a polychromatic beam allows collecting multiple spots from multiple grains in a single exposure as well as several spots corresponding to different crystallographic planes {hkl} of a single grain.
Each spot provides an image of the crystal generated by the beam diffracted by the {hkl} plane family of a grain, called topograph [59]. These Bragg spots are then characterized by the hkl Miller indices of the diffracting plane and by the projection of the diffraction vector→g (reciprocal lattice vector), indicating the orientation of the spot with respect to the position of the direct beam. This technique can obviously give information on the crystallographic orientations of the grains considering the relative position of the diffraction spots, but its major output concerns the internal structure of the individual spots as they contain information on misorientations, strain, and by extension on the presence of structural defects in general. Indeed, this is a powerful technique that can be used for the visualization of defects (dislocations, twins, domain walls, inclusions, impurity distribution) present in the crystal volume as it records their long-range distortion fields and/or the strain fields associated with a macroscopic crystal deformation. However, one drawback of the technique is the complex analysis of the obtained images which are distorted images of the crystals. The origin of the contrast observed in the images is briefly explained here, the reader is directed to several references for more details [9,59–62].
Due to the small beam divergence of the incoming synchrotron X-ray beam and to its large size, the whole width of the samples can be illuminated providing images exhibiting a minimum geometrical deformation effect. In our case, the diffracting volume corresponds to the width of the sample × the height of the field of view (generally 10 mm) × the thickness of the sample. It is worth noting that contrarily to more classical diffraction configurations, a limited number of diffraction spots can be collected during our experiments. This is due to both the distance between the sample and the diffraction pattern detector and the detector size. Indeed, although distance minimization is always possible to some extent, some hard limits are imposed by the DS furnace vacuum chamber needed to run solidification experiments. It explains why only a few diffraction spots are recorded on the films when they are used to record the diffraction pattern.
A few mechanisms are responsible for the contrast and intensity on the X-ray topographs we recorded. They are structure factor contrast, orientation contrast, and the so-called “direct image” mechanism. All of them derive from diffraction theory and Bragg’s law as explained for example in [63] and are evidenced in Figure2; Figure3.
2.2. Orientation Contrast
A particularly clear illustration of the orientation contrast is given in the presence of twins observed in our experiments (Figures2and3) [46,50].
Crystals 2020, 10, 555 8 of 25 single exposure as well as several spots corresponding to different crystallographic planes {hkl} of a single grain.
Each spot provides an image of the crystal generated by the beam diffracted by the {hkl} plane family of a grain, called topograph [59]. These Bragg spots are then characterized by the hkl Miller indices of the diffracting plane and by the projection of the diffraction vector 𝒈⃗ (reciprocal lattice vector), indicating the orientation of the spot with respect to the position of the direct beam. This technique can obviously give information on the crystallographic orientations of the grains considering the relative position of the diffraction spots, but its major output concerns the internal structure of the individual spots as they contain information on misorientations, strain, and by extension on the presence of structural defects in general. Indeed, this is a powerful technique that can be used for the visualization of defects (dislocations, twins, domain walls, inclusions, impurity distribution) present in the crystal volume as it records their long-range distortion fields and/or the strain fields associated with a macroscopic crystal deformation. However, one drawback of the technique is the complex analysis of the obtained images which are distorted images of the crystals. The origin of the contrast observed in the images is briefly explained here, the reader is directed to several references for more details [9,59–62].
Due to the small beam divergence of the incoming synchrotron X-ray beam and to its large size, the whole width of the samples can be illuminated providing images exhibiting a minimum geometrical deformation effect. In our case, the diffracting volume corresponds to the width of the sample × the height of the field of view (generally 10 mm) × the thickness of the sample. It is worth noting that contrarily to more classical diffraction configurations, a limited number of diffraction spots can be collected during our experiments. This is due to both the distance between the sample and the diffraction pattern detector and the detector size. Indeed, although distance minimization is always possible to some extent, some hard limits are imposed by the DS furnace vacuum chamber needed to run solidification experiments. It explains why only a few diffraction spots are recorded on the films when they are used to record the diffraction pattern.
A few mechanisms are responsible for the contrast and intensity on the X-ray topographs we recorded. They are structure factor contrast, orientation contrast, and the so-called “direct image” mechanism. All of them derive from diffraction theory and Bragg’s law as explained for example in [63] and are evidenced in Figure 2; Figure 3.
2.2. Orientation Contrast
A particularly clear illustration of the orientation contrast is given in the presence of twins observed in our experiments (Figures 2 and 3) [46,50].
Figure 2. X-ray diffraction images (topographs) recorded during solidification (applied temperature gradient: 30 K/cm and cooling rate of -1 K/min applied on both heaters at t0) from a FZ seed. (a)
Crystallographic orientation of the seed. (b) Laue pattern recorded at the end of solidification showing the diffraction spots in the field of view. Images of the (c) 111 and (d) 220 topographs recorded at two instants during solidification.
Figure 2.X-ray diffraction images (topographs) recorded during solidification (applied temperature gradient: 30 K/cm and cooling rate of −1 K/min applied on both heaters at t0) from a FZ seed.
(a) Crystallographic orientation of the seed. (b) Laue pattern recorded at the end of solidification showing the diffraction spots in the field of view. Images of the (c) 111 and (d) 220 topographs recorded at two instants during solidification.
Indeed, in the case of twinning during growth, the diffraction images are very different depending on the diffraction spots as can be seen in Figure2. A typical hatched aspect is observed for the diffraction spots corresponding to some {hkl} family planes as can be seen in Figure2b (e.g., α, β, and χ). The diffraction spot χ 220 shows a diffraction spot corresponding to {hkl} family planes which are not common with twinned grains that developed on both right- and left-hand sides of the sample (Figure2c). The complementary image corresponding to the twinned grains on the left (Figure2b β) is found at another position of the diffraction pattern, whereas the diffraction spot α 111 includes the diffraction patterns of the common family planes of the central main grain and of the twinned grains on the left (Figure2d). This is a particularly important element to be kept in mind when analyzing the topographs. Indeed, the observation of a single diffraction spot can be misleading. This is one of the reasons why several diffraction spots must be analyzed to be able to conclude.
Orientation contrast can also be produced, for instance when the sample displays sub-grain boundaries. For a monochromatic beam, the region corresponding to a {hkl} plane family is imaged at a position given by the Bragg’s law. Regions of different crystallographic orientations are not seen simultaneously on the diffraction image and appear as non-illuminated (white) zones. When a polychromatic beam is used, the misoriented regions are all in diffraction position simultaneously, but for different wavelengths. The images diffracted by neighboring sub-grains can exhibit a contrast associated with geometrical local superimpositions or separations of the diffracted beams on the topographs, according to the dimensions of the misoriented zone and to the value of the misorientation.
Additionally, crystalline defects such as precipitates, dislocations, and impurities, act on the diffraction process through their associated effective misorientation angle variation δθm(
→ r), which can be approximated by Equation (2) [60,62]: δθm( → r) = δd d ( → r)tanθB±δθ( → r) (2)
whereθBis the Bragg angle, δdd( →
r)is the local relative change of the lattice parameter andδθ(→r), the local change in crystallographic orientation. The double sign has to be chosen to take into account the effect of the deformation on the Bragg angle (decrease or increase of its value). This effective misorientation corresponds to the strain field generated by the defect, which is at the origin of Bragg diffraction of components of the incident beam that do not participate in the diffraction for the perfect crystal matrix [45,61]. This is the “direct image” mechanism that leads, in the X-ray low absorption case we are concerned with, to supplementary diffracted intensity associated to distorted regions. Andrew Lang developed this technique and revealed dislocations in silicon in his pioneer work [59].
The diffraction imaging technique was also used by Oriwol et al. [26] to study dislocations and the formation of sub-grain boundaries ex situ in Si ingots. Indeed, diffraction imaging applied to silicon crystals have proven to give unique insights into the evolution of dislocations [64,65] and cracks [66]. As can be understood from the above, one of the main advantages of diffraction imaging is that it can reveal low scale structural defects like dislocations on wide field images encompassing complete crystals as shown for example for diamonds by Burns et al. [61] and for Si [45,52,67].
An illustration is shown in Figure3c. In this topograph corresponding to the 111 diffraction spot
and recorded during the solidification from a silicon FZ seed (orientation Figure3a), black contrasts revealing deformation of the crystal structure are present at several places. Moreover, the deformation due to single dislocations can be clearly revealed in the seed and above the seed–regrown interface.
Crystals 2020, 10, 555 9 of 25
Figure 3. X-ray diffraction imaging (topography) during solidification (applied temperature gradient: 30 K/cm and cooling rate of -1 K/min applied on both heaters) from a FZ seed. (a) Crystallographic orientation of the seed. (b) Laue pattern showing the diffraction spots recorded at the end of solidification in the field of view. (c) Topograph of the 111 diffraction spot during solidification.
Importantly, if the strain field created around a defect is related to particular crystallographic orientations, it is not visible in all diffraction spot images (topographs). Indeed, if the displacement vector is perpendicular to the diffraction vector, the defect is not visible on the topograph. This is the case of dislocations whose image is extinct for the diffraction spots corresponding to diffraction vectors perpendicular to the Burgers vectors as also seen in TEM investigations [68,69]. On the one hand, this means that the absence of a dislocation strain field on a single diffraction spot does not mean that no dislocations are present. Depending on the dislocation character, at least two diffraction spots with different diffraction vectors perpendicular to each other must be analyzed before being able to conclude on the presence or not of dislocations. On the other hand, extinction is a powerful method to retrieve the Burgers vector direction as explained in detail for example in [70].
2.3. Dynamic Evolution
Another main originality of the experimental configuration we use is that several Laue patterns or topographs are recorded during a solidification experiment [45,46,71]. Then, it is possible to obtain sequences showing the evolution with time of the Laue pattern and of the topographs during the development of the grains. Such sequences allow a better understanding of the competition between the grains and of the occurrence of the twinning phenomenon. At the same time, the dynamics of the formation and evolution of defects as dislocations is followed during growth. The study of the growth of individual grains is then possible, along with the development of strain fields produced in the crystal structure by the structural defects. The combination of both imaging techniques and of the DS furnace provides complementary information on the dynamics of crystal growth and competition and on the deformation of the crystal structure.
Up to 2018, both in situ and real time X-ray imaging techniques, X-ray radiography and Bragg diffraction imaging (topography), were used alternately during growth. In this configuration, the different diffraction spots are collected on photographic films positioned after the furnace regularly during the experiment thanks to a specially designed device. X-ray diffracted beams are successively recorded on X-ray sensitive films (AGFA Structurix D3-SC, 17.6 × 12.5 cm2) positioned at a distance about 300 mm from the sample. The exposure time used to record the diffraction patterns is usually 0.5 s. In this configuration, radiographs and topographs are thus recorded alternately.
In 2018, we implemented together with the ESRF ID19 team a solution to record simultaneously radiographs and diffraction images (topographs). In this configuration, a scientific CMOS camera lens-coupled to a LuAG scintillator (commercial Ce-doped Lu3Al5O12, Crytur company—Czech Republic) is used to record the images of one of the diffraction spots (topograph). The camera has 2048 × 2048 pixels with a nominal pixel size of 6.5 µm2 and a dynamic range of 16 bit. It is coupled with a × 1.5 optic to decrease the pixel size to 4.3 µm2. In this new configuration, images recorded from both modes are fully synchronized. The image acquisition rate is of two frames per second in
Figure 3.X-ray diffraction imaging (topography) during solidification (applied temperature gradient: 30 K/cm and cooling rate of −1 K/min applied on both heaters) from a FZ seed. (a) Crystallographic orientation of the seed. (b) Laue pattern showing the diffraction spots recorded at the end of solidification in the field of view. (c) Topograph of the 111 diffraction spot during solidification.
Importantly, if the strain field created around a defect is related to particular crystallographic orientations, it is not visible in all diffraction spot images (topographs). Indeed, if the displacement vector is perpendicular to the diffraction vector, the defect is not visible on the topograph. This is the case of dislocations whose image is extinct for the diffraction spots corresponding to diffraction vectors perpendicular to the Burgers vectors as also seen in TEM investigations [68,69]. On the one hand, this means that the absence of a dislocation strain field on a single diffraction spot does not mean that no dislocations are present. Depending on the dislocation character, at least two diffraction spots with different diffraction vectors perpendicular to each other must be analyzed before being able to conclude on the presence or not of dislocations. On the other hand, extinction is a powerful method to retrieve the Burgers vector direction as explained in detail for example in [70].
2.3. Dynamic Evolution
Another main originality of the experimental configuration we use is that several Laue patterns or topographs are recorded during a solidification experiment [45,46,71]. Then, it is possible to obtain sequences showing the evolution with time of the Laue pattern and of the topographs during the development of the grains. Such sequences allow a better understanding of the competition between the grains and of the occurrence of the twinning phenomenon. At the same time, the dynamics of the formation and evolution of defects as dislocations is followed during growth. The study of the growth of individual grains is then possible, along with the development of strain fields produced in the crystal structure by the structural defects. The combination of both imaging techniques and of the DS furnace provides complementary information on the dynamics of crystal growth and competition and on the deformation of the crystal structure.
Up to 2018, both in situ and real time X-ray imaging techniques, X-ray radiography and Bragg diffraction imaging (topography), were used alternately during growth. In this configuration,
the different diffraction spots are collected on photographic films positioned after the furnace regularly during the experiment thanks to a specially designed device. X-ray diffracted beams are successively recorded on X-ray sensitive films (AGFA Structurix D3-SC, 17.6 × 12.5 cm2) positioned at a distance about 300 mm from the sample. The exposure time used to record the diffraction patterns is usually 0.5 s. In this configuration, radiographs and topographs are thus recorded alternately.
In 2018, we implemented together with the ESRF ID19 team a solution to record simultaneously radiographs and diffraction images (topographs). In this configuration, a scientific CMOS camera lens-coupled to a LuAG scintillator (commercial Ce-doped Lu3Al5O12, Crytur company—Turnov, Czech Republic) is used to record the images of one of the diffraction spots (topograph). The camera has 2048 × 2048 pixels with a nominal pixel size of 6.5 µm2and a dynamic range of 16 bit. It is coupled with a × 1.5 optic to decrease the pixel size to 4.3 µm2. In this new configuration, images recorded from both modes are fully synchronized. The image acquisition rate is of two frames per second in experiments reported in [52] which is sufficient to follow the solidification front of the samples.
The choice of the diffraction vector of the recorded spots and the alignment of the camera with respect to the sample face is an important aspect because it influences the information that can be revealed from the recorded topographs. Ideally a spot with a high intensity induced by the crystal plane structure factor should be chosen to better reveal defects. A detailed description of the equipment and imaging methods and configurations (alternate or simultaneous recording) can also be found in our previous publications [49,50,52].
2.4. Ex Situ Complementary Investigations
After the last melting–solidification cycle, the samples are cooled down to room temperature and removed from the GaTSBI furnace. Ex situ electron backscatter diffraction (EBSD) measurements are performed using a FEG-SEM JEOL JSM 7001F equipped with a HKL Nordlys camera after mirror polishing down to 1 µm with diamond paste. A step size of either 7 or 0.7 µm is used depending on the studied area. In order to depict the three-dimensional orientation of the crystals in the sample, inverse pole figure (IPF) orientation maps are generated with respect to the three space directions: normal to the sample surface (z), transverse direction (y), and in the growth direction (x). Moreover, the coincidence site lattice map (CSL) is reconstructed to evidence the grain boundaries separating grains with a specific crystallographic relationship. In this paper,Σ3 <111> (red color in the maps), Σ9 <110> (blue), and Σ27a <110> (yellow) twin boundaries labelling refer to rotations around the <h k l> axis that satisfy the misorientation ranges given by the Brandon criterion, (60 ± 8.66)◦, (38.94 ± 5)◦ and (31.58 ± 2.89)◦, respectively. Additionally, the grain orientation spread (GOS) map is extracted as well from the EBSD results. The GOS map is constructed by calculating the difference between the orientation of each pixel in the grain and of the grain average orientation to evidence the distorted areas within a grain structure. A color code is used to depict the grains without deformation (perfect Si crystal appears in blue) and having an average crystal structure deformation (red color for the highest deformation).
3. Results and Discussion
3.1. {111} Facet Growth and Undercooling
Theoretical models of the {111} facet growth laws exist [72,73] and are related to the undercooling at the level of the {111} facets. However, the orders of magnitude of the undercooling values for the corresponding laws are very different, so that experimental validation is needed. Moreover, directional solidification is widely used for the fabrication of multi-crystalline ingots so that the knowledge of {111} facet dynamics needs to be known during DS. Moreover, it constitutes a critical building block to develop predictive and quantitative models [74–76]. At last, the presence of {111} facets at the solid–liquid interface leads to the occurrence of twinning ultimately competing with the central grain growing from the seed as will be discussed in the following. It is thus essential to understand their
mechanism of formation and the undercooling at their level which gives conditions for twin nucleation. Our main objective was, thus, to determine the contribution of the undercooling of the {111} facets at the solid–liquid interface during Si directional solidification. {111} facet growth laws are derived and then compared with theoretical growth models reported in the literature.
At the level of the solid–liquid interface, {111} facets appear at the sample edges and in grain boundary grooves. Grain boundary grooves are formed due to the encounter between a grain boundary and the solid–liquid interface [77]. From the theory [78], grain boundary grooves can be either facetted/facetted, facetted/rough, or rough/rough depending on the crystallographic orientation of the adjacent grains. Experimentally, we are able to characterize facetted/rough and facetted/facetted grain boundary grooves [48,51] with a large prevalence for the facetted/facetted configuration. However,
conclusions concerning the predominance of one or the other grain boundary groove type cannot be drawn from these observations as rough/rough grain boundary grooves are expected to correspond to lower undercoolings compared to facetted/facetted ones and thus to smaller depth that can then fall below the spatial resolution used in these experiments.
Whatever conditions, facets observed in our experiments are always {111} facets as foreseen in silicon [79]. It was checked by determining the crystallographic orientation of the grains and their relative {111} facet orientation. In order to determine {111} facet growth laws, the facetted/facetted grain boundary grooves observed at the solid–liquid interface (e.g., in Figures1and4) were geometrically characterized by their angle and depth [80]. The geometrical parameters of the grain boundary grooves can be measured directly on the radiography images collected during solidification (Figures1and4). The kinetic parameters, growth velocity of the interface, and normal growth velocity of the groove facets, are also measured thanks to the time-resolved observation of the solid–liquid interface evolution.
Crystals 2020, 10, 555 11 of 25 Whatever conditions, facets observed in our experiments are always {111} facets as foreseen in silicon [79]. It was checked by determining the crystallographic orientation of the grains and their relative {111} facet orientation. In order to determine {111} facet growth laws, the facetted/facetted grain boundary grooves observed at the solid–liquid interface (e.g., in Figures 1 and 4) were geometrically characterized by their angle and depth [80]. The geometrical parameters of the grain boundary grooves can be measured directly on the radiography images collected during solidification (Figures 1 and 4). The kinetic parameters, growth velocity of the interface, and normal growth velocity of the groove facets, are also measured thanks to the time-resolved observation of the solid–liquid interface evolution.
When comparing the growth rate of the global solid–liquid interface to the {111} facet growth rates, it appears first that the growth rates of the {111} facets both inside the grooves and at the edges are smaller than the one of the global solid–liquid interface. This is expected because of the slower kinetics of the {111} planes compared to the other crystallographic orientations so that they are lagging behind other growing orientations and generally behind the global solid–liquid interface [47]. A major consequence is that the undercooling is higher in the groove and at the level of the edge facets compared to the undercooling at the level of the global solid–liquid interface. This favors nucleation events inside grooves and at the edge facets that are indeed often observed in real time during our experiments.
Figure 4. X-ray radiography images recorded during solidification, applied temperature gradient: 30 K/cm and cooling rate = −1 K/min applied on both heaters. Typical facetted/facetted grain boundary groove revealed by division by successive images.
The dynamics of a facetted/facetted groove during solidification can be seen for example in Figure 4. Both facets grow at the same growth rate as can be concluded from the constant angle and orientation of the groove. This conclusion is also sustained by the X-ray radiography images contrast (Figure 4). The white areas on the facets evidence the new grown solid between two successive images because of the image processing performed as explained in the experimental section. These white regions have the same thickness on both facets which indicates that both facets grow at the same rate. This is observed in all studied cases for facetted/facetted grain boundary grooves (see e.g., [48,51]).
The maximum thermal undercooling inside a grain boundary groove can be calculated knowing the local temperature gradient and the maximum grain boundary groove depth. Details of the calculations can be found in [48]. The measured maximum undercooling was, thus, calculated inside grain boundary grooves for several experiments with seeds oriented along <100>, <111> and <110> directions. In all cases, the maximum undercooling inside the grain boundary groove is found to be always lower than 1 K ranging from 1 × 10−1 to 4 × 10−1 K and adds to the solid–liquid interface undercooling [47]. Eventually, the mean facet velocity evolution as a function of the additional undercooling inside the grain boundary grooves can be obtained.
Figure 4. X-ray radiography images recorded during solidification, applied temperature gradient: 30 K/cm and cooling rate = −1 K/min applied on both heaters. Typical facetted/facetted grain boundary groove revealed by division by successive images.
When comparing the growth rate of the global solid–liquid interface to the {111} facet growth rates, it appears first that the growth rates of the {111} facets both inside the grooves and at the edges are smaller than the one of the global solid–liquid interface. This is expected because of the slower kinetics of the {111} planes compared to the other crystallographic orientations so that they are lagging behind other growing orientations and generally behind the global solid–liquid interface [47]. A major consequence is that the undercooling is higher in the groove and at the level of the edge facets compared to the undercooling at the level of the global solid–liquid interface. This favors nucleation events inside grooves and at the edge facets that are indeed often observed in real time during our experiments.
The dynamics of a facetted/facetted groove during solidification can be seen for example in Figure4. Both facets grow at the same growth rate as can be concluded from the constant angle and orientation of the groove. This conclusion is also sustained by the X-ray radiography images contrast (Figure4). The white areas on the facets evidence the new grown solid between two successive images
because of the image processing performed as explained in the experimental section. These white regions have the same thickness on both facets which indicates that both facets grow at the same rate. This is observed in all studied cases for facetted/facetted grain boundary grooves (see e.g., [48,51]).
The maximum thermal undercooling inside a grain boundary groove can be calculated knowing the local temperature gradient and the maximum grain boundary groove depth. Details of the calculations can be found in [48]. The measured maximum undercooling was, thus, calculated inside grain boundary grooves for several experiments with seeds oriented along<100>, <111> and <110> directions. In all cases, the maximum undercooling inside the grain boundary groove is found to be always lower than 1 K ranging from 1 × 10−1to 4 × 10−1K and adds to the solid–liquid interface undercooling [47]. Eventually, the mean facet velocity evolution as a function of the additional undercooling inside the grain boundary grooves can be obtained.
Moreover, {111} facets are also observed at the level of the solid–liquid interface at the sample edges as can be seen in Figures1c and5. The same procedure is applied to the {111} facets at the edges of the samples except that there is only one facet to consider in this case.
Crystals 2020, 10, 555 12 of 25 Moreover, {111} facets are also observed at the level of the solid–liquid interface at the sample edges as can be seen in Figures 1c and 5. The same procedure is applied to the {111} facets at the edges of the samples except that there is only one facet to consider in this case.
Figure 5. X-ray radiography images of the solid–liquid interface during growth with {111} facets at both edges of the sample for the experiments: (a) same experiment as in Figures 2 and 6a, (b) same experiment as in Figure 6c. Red lines indicate the traces of {111} planes.
At the level of the edge facets, the measured maximum undercooling is again always lower than 1 K. However, higher values (ranging from 2 × 10−1 to 8 × 10−1 K) compared to the undercooling inside grain boundary grooves are measured at the edges. This result is significant because the same evolution is obtained for several samples and for both grooves at the edges independently from possible sample particularities. The higher undercooling measured at the level of the edge {111} facets has a significant impact on the grain structure obtained at the end of solidification as it increases the nucleation probability during growth at the level of the edge facets. This is clearly confirmed by the grain structure obtained in the samples at the end of the experiments for which twin nucleation is frequent at the far edges of the facets (Figure 6). This major contribution of twins nucleating on edge {111} facets to grain competition and final grain structure was previously reported [7,45] and was observed repeatedly in our experiments.
The undercooling inside the grain boundary grooves and at the level of edge facets is always lower than 1 K relatively to the global solid–liquid interface which is far smaller than the undercooling values predicted by the bi-dimensional laws (several K) for the growth rates measured during these experiments. As a consequence, bi-dimensional nucleation growth mechanism [72] can be excluded. The experimental results concerning {111} facets kinetics in our experiments can only be compared favorably to the theoretical law corresponding to a growth mechanism eased by the presence of dislocations proposed by Voronkov [73]. This is in agreement with the fact that dislocations are expected to be easily generated during silicon growth and found emerging at the level of facets as shown for example in [45,81] and as can be seen in Figure 3.
3.2. Twinning During Solidification
As discussed in the introduction, the crystalline quality of the ingot and the grain boundary types, in particular the twin boundary characteristics, can have a significant impact on the photoelectric properties [22,27]. It has been shown that perfect symmetric Σ3 twins have no major impact on the photovoltaic performance. However, the repetition of twinning has important consequences for the final grain structure and distribution of crystallographic orientations [31]. Indeed, the importance of twinning in the development of the grain structure has been highlighted for different solidification processes ranging from directional solidification [82] to ribbon growth [33,83,84]. In the past few years, we studied rather extensively twin formation, growth, and its consequences on the final grain structure and defect formation in general [44–46,48,50,52,85].
3.2.1. Twin Nucleation
Four typical final grain structures of samples solidified from a seed in the GaTSBI DS furnace are shown in Figure 6. The coincidence site lattice maps (middle line in Figure 6) are shown in order to reveal the grain boundary character and in particular the twin boundaries. These samples are solidified from float-zone (FZ) monocrystalline seeds (Figure 6a,b) and from Czochralski (Cz) seeds
Figure 5.X-ray radiography images of the solid–liquid interface during growth with {111} facets at both edges of the sample for the experiments: (a) same experiment as in Figures2and6a, (b) same experiment as in Figure6c. Red lines indicate the traces of {111} planes.
At the level of the edge facets, the measured maximum undercooling is again always lower than 1 K. However, higher values (ranging from 2 × 10−1 to 8 × 10−1 K) compared to the undercooling inside grain boundary grooves are measured at the edges. This result is significant because the same evolution is obtained for several samples and for both grooves at the edges independently from possible sample particularities. The higher undercooling measured at the level of the edge {111} facets has a significant impact on the grain structure obtained at the end of solidification as it increases the nucleation probability during growth at the level of the edge facets. This is clearly confirmed by the grain structure obtained in the samples at the end of the experiments for which twin nucleation is frequent at the far edges of the facets (Figure6). This major contribution of twins nucleating on edge {111} facets to grain competition and final grain structure was previously reported [7,45] and was
observed repeatedly in our experiments.
The undercooling inside the grain boundary grooves and at the level of edge facets is always lower than 1 K relatively to the global solid–liquid interface which is far smaller than the undercooling values predicted by the bi-dimensional laws (several K) for the growth rates measured during these experiments. As a consequence, bi-dimensional nucleation growth mechanism [72] can be excluded. The experimental results concerning {111} facets kinetics in our experiments can only be compared favorably to the theoretical law corresponding to a growth mechanism eased by the presence of dislocations proposed by Voronkov [73]. This is in agreement with the fact that dislocations are expected to be easily generated during silicon growth and found emerging at the level of facets as shown for example in [45,81] and as can be seen in Figure3.
3.2. Twinning During Solidification
As discussed in the introduction, the crystalline quality of the ingot and the grain boundary types, in particular the twin boundary characteristics, can have a significant impact on the photoelectric properties [22,27]. It has been shown that perfect symmetricΣ3 twins have no major impact on the
photovoltaic performance. However, the repetition of twinning has important consequences for the final grain structure and distribution of crystallographic orientations [31]. Indeed, the importance of twinning in the development of the grain structure has been highlighted for different solidification processes ranging from directional solidification [82] to ribbon growth [33,83,84]. In the past few years, we studied rather extensively twin formation, growth, and its consequences on the final grain structure and defect formation in general [44–46,48,50,52,85].
3.2.1. Twin Nucleation
Four typical final grain structures of samples solidified from a seed in the GaTSBI DS furnace are shown in Figure6. The coincidence site lattice maps (middle line in Figure6) are shown in order to reveal the grain boundary character and in particular the twin boundaries. These samples are solidified from float-zone (FZ) monocrystalline seeds (Figure6a,b) and from Czochralski (Cz) seeds (Figure6c,d) after partial melting of the seed. The samples are solidified from seeds with different crystallographic orientations in the growth direction (Figure6bottom line). In all cases, side twins develop at the edges from {111} facets and compete with the main central grain issued from the seed, as it was also observed by Trempa et al. [7] in a systematic study. The fact that the behavior of FZ and Cz seeds is comparable suggests that the presence of oxygen (typically: 0.5–1 × 1018at/cm3in Cz ingots compared to<1015 at/cm3in FZ ingots) is not a predominant factor for the twin nucleation.
Crystals 2020, 10, 555 13 of 25 (Figure 6c,d) after partial melting of the seed. The samples are solidified from seeds with different crystallographic orientations in the growth direction (Figure 6 bottom line). In all cases, side twins develop at the edges from {111} facets and compete with the main central grain issued from the seed, as it was also observed by Trempa et al. [7] in a systematic study. The fact that the behavior of FZ and Cz seeds is comparable suggests that the presence of oxygen (typically: 0.5–1 × 1018 at/cm3 in Cz ingots compared to < 1015 at/cm3 in FZ ingots) is not a predominant factor for the twin nucleation.
Figure 6. Ex situ electron backscatter diffraction (EBSD) measurements revealing the grain structure and twin boundaries after growth and cooling down in samples grown from monocrystalline seeds. Applied temperature gradient: 30 K/cm and cooling rate applied on both heaters (a) −1 K/min (same experiment as in Figures 2, 8ab, and 9), (b) −1 K/min, (c) −0.2 K/min (same experiment as in Figures 7b and 8c–e), (d) applied temperature gradient: 20 K/cm and cooling rate: −0.2 K/min (same experiment as in Figure 7a). Top: Inverse Pole Figure (IPF) map along the growth direction. Middle: CSL (Coincidence Site Lattice) map. Bottom: Seed orientation and {111} planes.
Figure 5a,b corresponds to a snapshot at one instant during solidification showing the solid– liquid interface of samples in Figure 6a,c, respectively. The in situ X-ray radiography images (Figure 5) reveals that the solid–liquid interface is smooth during growth under these conditions for both Cz (Figure 5a) and FZ (Figure 5b) seeds. No destabilization of the interface can be observed in all cases when Cz or FZ seeds are used. Interface destabilization has only been observed in the presence of Cu impurities as reported in [53].
Despite the global smooth interface, {111} facets can be clearly seen on the X-ray radiography images at the edges of the sample (Figure 5). It was verified that they correspond to the projection of {111} facets by determining the corresponding pole figures using the measurements performed by EBSD. The {111} facet orientation is highlighted by the red lines in Figure 5. Twin nucleation takes place regularly on these {111} facets as can be seen for example in Figure 5a (right) and Figure5b (left). A video of radiograph images showing the dynamic evolution of the solid–liquid interface during the experiment corresponding to Figures 2, 5a, and 6a is provided as supplementary material (Video S1). It evidences twin nucleation at the {111} edge facets and the formation of grain boundary grooves at the solid–liquid interface due to the subsequent grain competition.
Diffraction spot images collected at different times during the solidification of the two samples (corresponding to the experiments and grain structure in Figure 6c,d) are shown in Figure 7. The diffraction spots in Figure 7a display the twinning zone at the right side of the sample in Figure 6d, whereas the diffraction spots in Figure 7b display the twinning zone at the left side of the sample in Figure 6c. The purple dotted line is added in Figure 7a to indicate the corresponding solid–liquid interface shape as observed in the radiographs. It is worth reminding that diffraction imaging shows only the crystalline solid areas. The observation of the upper part of the diffraction spots shows that the twin nucleation occurs at the edges of the samples at the solid–liquid-vacuum-crucible phase line
Figure 6.Ex situ electron backscatter diffraction (EBSD) measurements revealing the grain structure and twin boundaries after growth and cooling down in samples grown from monocrystalline seeds. Applied temperature gradient: 30 K/cm and cooling rate applied on both heaters (a) −1 K/min (same experiment as in Figure2, Figure 8a,b, and Figure 9), (b) −1 K/min, (c) −0.2 K/min (same experiment as
in Figure7b and Figure 8c–e), (d) applied temperature gradient: 20 K/cm and cooling rate: −0.2 K/min
(same experiment as in Figure7a). Top: Inverse Pole Figure (IPF) map along the growth direction. Middle: CSL (Coincidence Site Lattice) map. Bottom: Seed orientation and {111} planes.
Figure5a,b corresponds to a snapshot at one instant during solidification showing the solid–liquid interface of samples in Figure6a,c, respectively. The in situ X-ray radiography images (Figure5) reveals that the solid–liquid interface is smooth during growth under these conditions for both Cz (Figure5a) and FZ (Figure5b) seeds. No destabilization of the interface can be observed in all cases when Cz or FZ seeds are used. Interface destabilization has only been observed in the presence of Cu impurities as reported in [53].
Despite the global smooth interface, {111} facets can be clearly seen on the X-ray radiography images at the edges of the sample (Figure5). It was verified that they correspond to the projection of {111} facets by determining the corresponding pole figures using the measurements performed by
